scholarly journals Production, Replenishment and Inventory Policies for Perishable Products in a Two-Echelon Distribution Network

2020 ◽  
Vol 12 (11) ◽  
pp. 4735
Author(s):  
Mingyuan Wei ◽  
Hao Guan ◽  
Yunhan Liu ◽  
Benhe Gao ◽  
Canrong Zhang
Keyword(s):  
Inventory Management ◽  
Valid Inequalities ◽  
Distribution Network ◽  
Planning Horizon ◽  
Branch And Cut ◽  
Computational Time ◽  
Perishable Products ◽  
Inventory Cost ◽  
Routing Problem ◽  
Selection Of

The research on production, delivery and inventory strategies for perishable products in a two-echelon distribution network integrates the production routing problem (PRP) and two-echelon vehicle routing problem (2E-VRP), which mainly considers the inventory and delivery sustainability of perishable products. The problem investigated in this study is an extension of the basic problems, and it simultaneously optimizes production, replenishment, inventory, and routing decisions for perishable products that will deteriorate over the planning horizon. Additionally, the lead time has been considered in the replenishment echelon, and the unit inventory cost varying with the inventory time is considered in the inventory management. Based on a newly designed model, different inventory strategies are discussed in this study: old first (OF) and fresh first (FF) strategies both for the first echelon and second echelon, for which four propositions to model them are proposed. Then, four valid inequalities, including logical inequalities, a ( ℓ , S , W W ) inequality, and a replenishment-related inequality, are proposed to construct a branch-and-cut algorithm. The computational experiments are conducted to test the efficiency of valid inequalities, branch-and-cut, and policies. Experimental results show that the valid inequalities can effectively increase the relaxed lower bound by 4.80% on average and the branch-and-cut algorithm can significantly reduce the computational time by 58.18% on average when compared to CPLEX in small and medium-sized cases. For the selection of strategy combinations, OF–FF is suggested to be used in priority.

A Benders Decomposition Approach for the Multivehicle Production Routing Problem with Order-up-to-Level Policy

2020 ◽  
Author(s):  
Zhenzhen Zhang ◽  
Zhixing Luo ◽  
Roberto Baldacci ◽  
Andrew Lim
Keyword(s):  
Benders Decomposition ◽  
Valid Inequalities ◽  
Planning Horizon ◽  
Set Partitioning ◽  
Master Problem ◽  
Inventory Level ◽  
Inventory Routing ◽  
Routing Problem ◽  
Decomposition Approach ◽  
Production Routing

The production routing problem (PRP) arises in the applications of integrated supply chain which jointly optimize the production, inventory, distribution, and routing decisions. The literature on this problem is quite rare due to its complexity. In this paper, we consider the multivehicle PRP (MVPRP) with order-up-to-level inventory replenishment policy, where every time a customer is visited, the quantity delivered is such that the maximum inventory level is reached. We propose an exact Benders’ decomposition approach to solve the MVPRP, which decomposes the problem as a master problem and a slave problem. The master problem decides whether to produce the product, the quantity to be produced, and the customers to be replenished for every period of the planning horizon. The resulting slave problem decomposes into a capacitated vehicle routing problem for each period of the planning horizon where each problem is solved using an exact algorithm based on the set partitioning model, and the identified feasibility and optimality cuts are added to the master problem to guide the solution process. Valid inequalities and initial optimality cuts are used to strengthen the linear programming relaxation of the master formulation. The exact method is tested on MVPRP instances and on instances of the multivehicle vendor-managed inventory routing problem, a special case of the MVPRP, and the good performance of the proposed approach is demonstrated.

scholarly journals Cover Inequalities for a Vehicle Routing Problem with Time Windows and Shifts

2019 ◽  
Vol 53 (5) ◽  
pp. 1354-1371 ◽  
Author(s):  
Said Dabia ◽  
Stefan Ropke ◽  
Tom van Woensel
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Valid Inequalities ◽  
Time Windows ◽  
Branch And Cut ◽  
Master Problem ◽  
Loading Capacity ◽  
Routing Problem ◽  
Cover Inequalities ◽  
And Shifts

This paper introduces the vehicle routing problem with time windows and shifts (VRPTWS). At the depot, several shifts with nonoverlapping operating periods are available to load the planned trucks. Each shift has a limited loading capacity. We solve the VRPTWS exactly by a branch-and-cut-and-price algorithm. The master problem is a set partitioning with an additional constraint for every shift. Each constraint requires the total quantity loaded in a shift to be less than its loading capacity. For every shift, a pricing subproblem is solved by a label-setting algorithm. Shift capacity constraints define knapsack inequalities; hence we use valid inequalities inspired from knapsack inequalities to strengthen the linear programming relaxation of the master problem when solved by column generation. In particular, we use a family of tailored robust cover inequalities and a family of new nonrobust cover inequalities. Numerical results show that nonrobust cover inequalities significantly improve the algorithm.

scholarly journals Distribution Network Design for Fixed Lifetime Perishable Products: A Model and Solution Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Z. Firoozi ◽  
N. Ismail ◽  
Sh. Ariafar ◽  
S. H. Tang ◽  
M. K. A. M. Ariffin ◽  
...  
Keyword(s):  
Network Design ◽  
Distribution Network ◽  
Distribution Networks ◽  
Storage Conditions ◽  
Perishable Products ◽  
Inventory Cost ◽  
Solution Approach ◽  
Distribution Network Design ◽  
Large Size ◽  
Fixed Lifetime

Nowadays, many distribution networks deal with the distribution and storage of perishable products. However, distribution network design models are largely based on assumptions that do not consider time limitations for the storage of products within the network. This study develops a model for the design of a distribution network that considers the short lifetime of perishable products. The model simultaneously determines the network configuration and inventory control decisions of the network. Moreover, as the lifetime is strictly dependent on the storage conditions, the model develops a trade-off between enhancing storage conditions (higher inventory cost) to obtain a longer lifetime and selecting those storage conditions that lead to shorter lifetimes (less inventory cost). To solve the model, an efficient Lagrangian relaxation heuristic algorithm is developed. The model and algorithm are validated by sensitivity analysis on some key parameters. Results show that the algorithm finds optimal or near optimal solutions even for large-size cases.

scholarly journals Analysis of the effects of Lead-Time variation and Lateral Transshipment insertion in a Supply Chain Network

2021 ◽  
Author(s):  
Mohamed Salim Amri Sakhri ◽  
Mounira Tlili ◽  
Ouajdi Korbaa
Keyword(s):  
Supply Chain ◽  
Inventory Management ◽  
Planning Horizon ◽  
Inventory Level ◽  
Inventory Routing ◽  
Routing Problem ◽  
Network Cost ◽  
Lateral Transshipment ◽  
The Impact ◽  
Number Of Customers

Abstract In a supply chain, inventory is the single largest source of costs for a company. This is due to the various physical and informational activities that accompany inventory management, primarily the holding and transportation of inventory. Companies are looking to streamline these activities and minimize the associated costs. One of the most coveted models to jointly solve these two problems is the Inventory Routing Problem (IRP), which will be the focus of this study. This paper addresses the case of a deterministic replenishment demand in a distribution network consisting of a supplier and a number of customers to be served by a single vehicle over a finite planning horizon. We will first study the impact of increasing supplier lead times on network costs. Then, we will study the effects of the Lateral Transshipment (LT) technique on the overall network cost. A mathematical model is developed and solved by an exact method. The results obtained will show that LT is an effective tool capable of improving the total network cost and balancing the customers’ inventory level.

scholarly journals Mixed-integer programming approaches for the time-constrained maximal covering routing problem

OR Spectrum ◽  
2021 ◽  
Author(s):  
Markus Sinnl
Keyword(s):  
Integer Programming ◽  
Mixed Integer Programming ◽  
Valid Inequalities ◽  
Optimal Solution ◽  
Branch And Cut ◽  
Mixed Integer ◽  
Routing Problem ◽  
Maximal Covering ◽  
Solution Algorithms ◽  
Number Of Customers

AbstractIn this paper, we study the recently introduced time-constrained maximal covering routing problem. In this problem, we are given a central depot, a set of facilities, and a set of customers. Each customer is associated with a subset of the facilities which can cover it. A feasible solution consists of k Hamiltonian cycles on subsets of the facilities and the central depot. Each cycle must contain the depot and must respect a given distance limit. The goal is to maximize the number of customers covered by facilities contained in the cycles. We develop two exact solution algorithms for the problem based on new mixed-integer programming models. One algorithm is based on a compact model, while the other model contains an exponential number of constraints, which are separated on-the-fly, i.e., we use branch-and-cut. We also describe preprocessing techniques, valid inequalities and primal heuristics for both models. We evaluate our solution approaches on the instances from literature and our algorithms are able to find the provably optimal solution for 267 out of 270 instances, including 123 instances, for which the optimal solution was not known before. Moreover, for most of the instances, our algorithms only take a few seconds, and thus are up to five magnitudes faster than previous approaches. Finally, we also discuss some issues with the instances from literature and present some new instances.

scholarly journals Branch-Cut-and-Price for the Robust Capacitated Vehicle Routing Problem with Knapsack Uncertainty

2021 ◽  
Author(s):  
Artur Alves Pessoa ◽  
Michael Poss ◽  
Ruslan Sadykov ◽  
François Vanderbeck
Keyword(s):  
Combinatorial Optimization ◽  
Vehicle Routing ◽  
Demand Uncertainty ◽  
Optimization Problems ◽  
Valid Inequalities ◽  
Branch And Cut ◽  
Routing Problem ◽  
Combinatorial Optimization Problems ◽  
Robust Formulation ◽  
Capacitated Vehicle

Capacitated vehicle routing problems are widely studied combinatorial optimization problems, and branch-and-cut-and-price algorithms can solve instances harder than ever before. These models, however, neglect that demands volumes are often not known with precision when planning the vehicle routes, thus incentivizing decision makers to significantly overestimate the volumes for avoiding coping with infeasible routes. A robust formulation that models demand uncertainty through a knapsack polytope is considered. A new branch-and-cut-and-price algorithm for the problem is provided, which combines efficient algorithms for the problem with no uncertainty with profound results in robust combinatorial optimization and includes novel heuristics and new valid inequalities. The numerical results illustrate that the resulting approach is two orders of magnitude faster that the best algorithm from the literature, solving twice as many instances to optimality.

Fuel Consumption Optimization Model for the Multi-Period Inventory Routing Problem

2018 ◽  
Vol 2672 (9) ◽  
pp. 59-69 ◽  
Author(s):  
Chun Cheng ◽  
Mingyao Qi ◽  
Louis-Martin Rousseau
Keyword(s):  
Fuel Consumption ◽  
Valid Inequalities ◽  
Transportation Cost ◽  
Integer Program ◽  
Branch And Cut ◽  
Inventory Routing ◽  
Fuel Price ◽  
Routing Problem ◽  
Inventory Routing Problem ◽  
Inventory Costs

In the traditional multi-period inventory routing problem (MIRP), traveling distance is considered as the only measurement of vehicles’ variable transportation cost; however, it is in fact the fuel consumption cost, not the distance, which is the greater concern. This paper evaluates vehicles’ variable transportation cost by fuel consumption, which is influenced by distance, load, and fuel price. It presents an integer program to formally characterize the fuel consumption considered MIRP (FCMIRP), which can help enterprises obtain a more accurate tradeoff between transportation and inventory costs. It also benefits the environment, because reducing fuel consumption will curb carbon dioxide (CO2) emissions. Valid inequalities are added to strengthen the model and use a branch-and-cut algorithm. Computational tests indicate that the FCMIRP can decrease fuel consumption and total cost over the traditional model. Factors that influence the results of FCMIRP are also discussed.

Is Hydraulics Over-Used or Under-Used in Storm Drainage?

1994 ◽  
Vol 29 (1-2) ◽  
pp. 53-61
Author(s):  
Ben Chie Yen
Keyword(s):  
Unsteady Flow ◽  
Computational Time ◽  
Time Step ◽  
Flow Routing ◽  
Kinematic Wave Equation ◽  
Storm Drainage ◽  
Saint Venant Equations ◽  
Unsteady Flow Routing ◽  
Selection Of

Urban drainage models utilize hydraulics of different levels. Developing or selecting a model appropriate to a particular project is not an easy task. Not knowing the hydraulic principles and numerical techniques used in an existing model, users often misuse and abuse the model. Hydraulically, the use of the Saint-Venant equations is not always necessary. In many cases the kinematic wave equation is inadequate because of the backwater effect, whereas in designing sewers, often Manning's formula is adequate. The flow travel time provides a guide in selecting the computational time step At, which in turn, together with flow unsteadiness, helps in the selection of steady or unsteady flow routing. Often the noninertia model is the appropriate model for unsteady flow routing, whereas delivery curves are very useful for stepwise steady nonuniform flow routing and for determination of channel capacity.

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